Phase Property of Envelope-Tracking EEG Response Is Preserved in Patients with Disorders of Consciousness

Abstract When listening to speech, the low-frequency cortical response below 10 Hz can track the speech envelope. Previous studies have demonstrated that the phase lag between speech envelope and cortical response can reflect the mechanism by which the envelope-tracking response is generated. Here, we analyze whether the mechanism to generate the envelope-tracking response is modulated by the level of consciousness, by studying how the stimulus-response phase lag is modulated by the disorder of consciousness (DoC). It is observed that DoC patients in general show less reliable neural tracking of speech. Nevertheless, the stimulus-response phase lag changes linearly with frequency between 3.5 and 8 Hz, for DoC patients who show reliable cortical tracking to speech, regardless of the consciousness state. The mean phase lag is also consistent across these DoC patients. These results suggest that the envelope-tracking response to speech can be generated by an automatic process that is barely modulated by the consciousness state.


Introduction
When listening to speech, a prominent cortical response is the response that tracks the speech envelope, i.e., lowfrequency fluctuation in sound intensity (Lalor et al., 2009;Ding and Simon, 2012a;Wang et al., 2012;Peelle et al., 2013;Doelling et al., 2014;Harding et al., 2019). The speech envelope is critical for speech intelligibility and prevalent in natural sounds (Drullman et al., 1994;Shannon et al., 1995;Shamma, 2001;Elliott and Theunissen, 2009;Ding et al., 2017). The speech envelope is extracted from the sound input in the auditory periphery (Yang et al., 1992;Shamma, 2001), and the low-frequency components of the speech envelope is amplified through the auditory processing pathway (Sharpee et al., 2011). Intracranial recordings have revealed that, in cortex, the low-frequency envelope-tracking neural response is observed both in auditory cortex and in other widely distributed temporal and frontal areas (E.M. Zion Golumbic et al., 2013b). Since the envelope-tracking response can be reliably measured from individuals and is an auditory response that receives the modulation from higher-order cortical areas, it has been applied widely to study auditory processing in special populations (Braiman et al., 2018;Xu et al., 2021).
The physiological interpretation of the envelope-tracking response, however, has been controversial. On the one hand, since the envelope-tracking response is phase locked to the speech input, it may purely reflect bottom-up sensory evoked responses (Steinschneider et al., 2013). Some studies further suggest that the bottom-up sensory mechanism generating the envelope-tracking response can be well approximated by a linear system (Lalor et al., 2009;Ding and Simon, 2012a,b). In other words, the envelopetracking response is well approximated as a superposition of the neural responses independently evoked by auditory features. This hypothesis is referred to as the evoked response hypothesis. On the other hand, the envelope-tracking response is strongly modulated by top-down attention (Ding and Simon, 2012b;Power et al., 2012;O'Sullivan et al., 2015), and is influenced by language proficiency , prior information (Wang et al., 2019), and multisensory input (E. Zion Golumbic et al., 2013a;Crosse et al., 2016). The strong top-down and multisensory modulation effects lead to the hypothesis that the envelope-tracking response reflects a modulation signal from higherlevel cortical areas, e.g., ventral prefrontal cortex (Schroeder et al., 2008;van Atteveldt et al., 2014;Giordano et al., 2017). Specifically, the modulation signal resets the phase of ongoing oscillations in, e.g., auditory cortex, so that the ongoing oscillations track the speech envelope. For this hypothesis, referred to as the oscillation phase resetting hypothesis, the phase of neural oscillations is an index for neural excitability (Lakatos et al., 2013). Consequently, when neural oscillations show a phase that indexes high neural excitability, the sensory input will be better encoded (Jeremy et al., 2011;van Atteveldt et al., 2014) and the high excitability phase is often referred to as the optimal phase (Schroeder et al., 2008;Henry and Obleser, 2012;Ng et al., 2012).
In the frequency domain, the neural response tracking speech envelope can be decomposed into response power and response phase at each frequency (Luo and Poeppel, 2007). Recent studies have shown that the response phase carries important information about how the envelope-tracking response is generated (Doelling et al., 2019;Zou et al., 2021). Suppose the envelope-tracking response is generated by purely bottom-up mechanisms: the auditory periphery extracts the speech envelope and envelope-tracking neural activity is transmitted from auditory nerves to auditory cortex. For such a purely bottom-up mechanism, neural activity in cortex tracks the speech envelope with a constant delay that corresponds to the neuronal transmission time and the time to generate large-scale synchronized cortical responses. In this condition, in the frequency domain, the stimulus-response phase lag is a linear function of response frequency. Evidence for such linear-phase property is previously observed in healthy individuals who passively listen to speech .
In contrast, if the mechanisms generating the envelopetracking response engage complex interactions between multiple cortical or subcortical areas, as is emphasized by the oscillation phase resetting hypothesis, the cortical response will not just be a delayed version of the speech envelope. Consequently, in the frequency domain, the stimulusresponse phase lag will not reduce to a simple linear function in general. In particular, when healthy individuals actively listen to music, it has been shown that the stimulus-response phase lag is around 0 degree across frequencies (Doelling et al., 2019), consistent with the hypothesis that an optimal, i.e., high-excitability, phase is always aligned to the stimulus regardless of its presentation frequency (Schroeder et al., 2008;Doelling et al., 2019).
For healthy individuals, the speech envelope-tracking response is influenced by both the bottom-up speech input and top-down feedback from higher-level cognitive systems. Therefore, it is challenging to tease apart whether the linear-phase property and latency of envelope-tracking activity is determined by bottom-up processes or an interaction between bottom-up sensory encoding and top-down feedback. Here, we investigate whether the response phase property and response latency are preserved when topdown cognitive modulation diminishes. To reduce topdown neural modulation, we test patients with disorder of consciousness (DoC), which is caused by extensive or focal injuries to neural tissues that lead to the large-scale dysfunctions of the central nervous system (Giacino et al., 2014). DoC patients can be further divided into groups who have different levels of consciousness, e.g., patients in the unresponsive wakefulness syndrome (UWS)/vegetative state (VS; Ashwal, 1994;Laureys et al., 2010), patients in the minimal conscious state (MCS; Giacino et al., 2002), and patients emerged from a minimally conscious state (EMCS). Here, we analyze whether the phase properties of the envelope-tracking response are influenced by the DoC, who can have preserved bottom-up auditory processing (Giacino et al., 2014;Beukema et al., 2016) but their top-down cognitive control is severely impaired (Daniel et al., 2016;Giacino et al., 2018). If the envelope-tracking response primarily reflects bottom-up processing, its phase property can be preserved in DoC patients. In contrast, if the envelope-tracking response critically relies on top-down neural modulation, its phase properties should be altered by the DoC.

Participants
This study analyzed the phase properties of envelopetracking neural activity based on an EEG dataset that included healthy individuals, MCS patients, and UWS patients . In addition, following the same experimental procedure in Xu et al. (2021), this study also collected data from EMCS patients. In total, data from 56 participants were reported (16 UWS: 12 males, 56.81 6 12.75 years; 15 MCS: 14 males, 49.07 6 16.55 years; 9 EMCS: 9 males, 50.78 6 13.64 years; 16 healthy individuals, 5 males; 54.25 6 9.88 years). There was no significant age difference between healthy individuals and any of the three patient populations (one-way ANOVA, p ¼ 0.339). No significant difference in brain injury duration was observed between the three patient populations (one-way ANOVA, p ¼ 0.224). The study was approved by the Ethical Committee of the First Affiliated Hospital of Zhejiang University, and by Hangzhou Mingzhou Brain Rehabilitation Hospital. Written informed consent was provided by participants or their legal surrogates for the experiments and for publication of their individual details in this study.

Stimuli and experimental procedures
Participants were exposed to natural speech through headphones in a patient room. The stimulus included two chapters from Cixin Liu's novel, The Supernova Era (Chapter 16: "Fun country" and Chapter 18: "Sweet dream period"). The speech was narrated in Mandarin Chinese by a female speaker and digitized at a 48-kHz sampling rate. The speech was clear and highly intelligible. The duration of the two chapters were 34 and 25 min, respectively, and responses to the two chapters were concatenated in analyses.
EEG response were recorded while participants listened to speech. The experiment was conducted in 2 d, and the spoken narrative was presented once on each day. The DoC participants had their eyes open at the beginning of each day's experiment. Both healthy individuals and EMCS patients were instructed to remain still throughout the experiment. No additional tasks or instructions were given.

EEG recording and preprocessing
EEG signals were recorded using a 64-electrodes BrainCap (Brain Products GmbH) following the international 10-20 system. One of these electrodes was positioned under the right eye to record electrooculogram (EOG). EEG signals were initially referenced online to FCz but were later referenced offline to a common average reference. To remove line noise, a 50-Hz notch filter was applied, along with a low-pass antialiasing filter with a 70-Hz cutoff and a high-pass filter with a 0.3-Hz cutoff to prevent slow drifts (both eighth order zeros-phase Butterworth filters). Signals were sampled at 1 kHz and processed according to the procedure detailed previously . All preprocessing and analysis were performed using MATLAB software (The MathWorks).
EEG recordings underwent low-pass filtering below 50 Hz using a zero-phase anti-aliasing FIR filter (implemented using a 200-ms Kaiser window) and downsampled to 100 Hz. EOG artifacts were eliminated through regression based on the least-squares method. The same as in previous studies (Ding and Simon, 2012a,b), the speech response was averaged over the two representations on both recording days to enhance the signal-tonoise ratio.
The speech envelope was obtained by applying fullwave rectification to the speech  and low-pass filtering it below 50 Hz using a zero-phase antialiasing FIR filter (implemented using a 200-ms Kaiser window). The envelope was further down-sampled to 100 Hz.

Phase extraction and phase coherence
To assess the stimulus-response phase lag, both the speech envelope and EEG response were converted into the frequency domain, with each electrode being independently analyzed. Specifically, the speech envelope and EEG response were divided into nonoverlapping 2-s time bins and subsequently transformed into the frequency domain using the discrete Fourier transform (DFT) via the fast Fourier transform (FFT) algorithm. The response phase (a ft ) and stimulus phase (b ft ) in frequency bin f and time bin t were used to determine the stimulus-response phase lag u ft as a ft À b ft . The coherence of the phase lag across time bins, referred to as the cerebro-acoustic phase coherence (Peelle et al., 2013), was computed using this equation: where C(f) was the phase coherence in frequency bin f. Greater phase coherence implies that the response phase more precisely follows the stimulus phase. With phase coherence being strongest in central-frontal electrodes for all participant groups (Fig. 1B), 14 centro-frontal electrodes (i.e., Fz, F1, F2, F3, F4, FC1, FC2, FC3, FC4, Cz, C1, C2, C3, and C4) were used to compare the phase coherence value across populations and examine the phasefrequency relationship.

Phase-frequency relationship
The stimulus-response phase lag at frequency f, denoted as u f , was computed by averaging u ft across all 2-s time bins using the circular mean (Fisher, 1993). Group delay is characterized based on the first-order derivative of the stimulus-response phase lag across frequency, i.e., d(f) ¼ (u (f) À u (f 1 Df))/2p Df (Oppenheim et al., 1997). The group delay was computed by unwrapping the phase lag, calculating the difference between adjacent frequency bins, and dividing the difference by p . The mean phase difference was computed À u (f 1 NDf))/Df/(N À 1). The mean phase was transformed into a group delay by dividing it by p .
To assess the linearity of the phase-frequency curve, the absolute value of its second-order derivative was calculated using the equation: A second-order derivative d 2 (f) of 0 would indicate a linear change in phase lag with frequency. Thus, d 2 (f) reflects the linearity of the phase-frequency curve, where lower d 2 (f) values indicate a more linear curve.
As the phase-frequency curve exhibited a near-linear relationship between 3.5 and 8 Hz, a linear function was used to approximate the actual phase-frequency curve within this range: u L (f) ¼ kf 1 b, for 3.5 f 8. The slope parameter k and the intercept parameter b were fitted separately for each participant population using the leastsquares method.

Statistics
In order to assess whether the phase coherence at a specific frequency was significantly greater than chance, we employed a permutation approach to estimate the chancelevel phase coherence (Peelle et al., 2013;Harding et al., 2019). After the speech envelope and EEG response were divided into 2-s time bins, the time bins for the speech envelope were shuffled, resulting in a random pairing of the envelope and response. Subsequently, we computed the phase coherence for the phase lag between the response and the randomly paired speech envelope. This process was conducted 5000 times, yielding 5000 chance-level phase coherence. For the significance tests in Figure 1A, we computed the averaged phase coherence value across electrodes and participants in each population, for both the actual phase coherence and the 5000 chance-level phase coherence. The significance level of the phase coherence at a specific frequency was (N 1 1)/5001, if it was lower than N out of the 5000 chance-level coherence at that frequency (one-sided comparison).
A similar procedure was used to determine the chancelevel second-order derivative of the phase-frequency curve. The second-order derivative was significantly nearer to 0 than chance, with the significance level being (N 1 1)/5001, if it was greater than N of the 5000 chancelevel values in terms of the absolute value (one-sided comparison).

Results
The current study aimed to analyze whether the phase lag between speech envelope and cortical response was a linear function of frequency. A prerequisite of the analysis is that the stimulus-response phase lag is reliably measured. Therefore, we first identified which frequency bands and EEG electrodes exhibited reliable phase synchronization between neural response and speech envelope. We computed the coherence of the stimulus-response phase lag for each electrode in each frequency bin separately, and the results in Figure 1A were averaged across all electrodes. Significant phase coherence was observed in at least one frequency bin below 9 Hz for all participant populations. The topography of the low-frequency neural responses (,9 Hz) showed a centro-frontal distribution for all 4 groups of participants (Fig. 1B). Therefore, we selected 14 centro-frontal channels for further analyses.
We next investigated how the stimulus-response phase lag varied with frequency. For healthy individuals, the phase lag appeared to change linearly with frequency in the range where the phase coherence exceeded chance levels ( Fig.  2A). The linearity of the phase-frequency curve was evaluated using its second-order derivative. For a linear function, the second-order derivative equaled 0. As shown in Figure 3A, the absolute value of second-order derivative of the phase-frequency curve was significantly closer to 0, i.e., lower than chance, between 3.5 and 8 Hz for healthy individuals (p , 0.01, permutation test, FDR corrected), suggesting a linear phase-frequency function. A straight line was used to fit this linear trend between 3.5 and 8 Hz and was shown by the dotted gray line in Figure 2.
The DoC patients showed a similar linear trend in the same frequency range (Fig. 2, lower three panels), although the curves were noisier because of the lower phase coherence (Fig. 1A). As shown in Figure 3A, for the EMCS and MCS patients, the second-order derivative of the phasefrequency curve was also significantly closer to 0 in some frequency bins between 3.5 and 8 Hz (p , 0.01, permutation test, FDR corrected). For the UWS patients, the second-order derivative showed a similar trend between 3.5 and 8 Hz, but the trend was not significant. It was observed Figure 1. Phase coherence spectrum. A, The phase coherence spectrum shows how precisely the response is synchronized to the stimulus. The colored lines on top denote frequency bins in which the phase coherence is significantly higher than chance (p , 0.01, permutation test, FDR corrected). Stimulus-response phase synchronization is significantly reliable below ;9 Hz. B, Topography of phase coherence. To better illustrate the spatial distribution, the phase coherence is separately normalized in each plot by dividing by the 95th percentile of phase coherence across electrodes, and the values of the 95th percentile is shown on top of each plot. The dark dots represent the 14 centro-frontal electrodes chosen for subsequent phase analysis. that the phase-frequency curve tended to be more linear for participants who showed higher phase coherence: when the absolute value of the second-order derivative was averaged between 3.5 and 8 Hz, it correlated with the individual phase coherence averaged over the same frequency range (R ¼ À0.767, p ¼ 5 Â 10 À11 , two-tailed Student's t test; Fig. 3B).
Based on the systems theory, the group delay is proportional to the first-order derivative of the phase-frequency function, reflecting how quickly a change in the stimulus is reflected in the response (Oppenheim et al., 1997). Based on the linear fit in Figure 2, the mean group delay between 3.5 and 8 Hz was 152, 147, 152, and 146 ms, for the healthy individuals, EMCS, MCS, and UWS patients, respectively. The group delay at each frequency was shown in Figure 4A for all four populations. Healthy individuals showed consistent group delay between 3.5 and 8 Hz (Fig. 4A, upper panel). For the DoC patients, the group delay appeared to have larger individual differences (Fig. 4A, lower three panels). The large individual difference could be attributed to at least two factors. First, different DoC patients had difference response latency. Second, the stimulus-response phase lag was not reliable. For an extreme case, if the neural response was not synchronized to the stimulus, the group delay would be completely random for each participant. To distinguish these two possibilities, we analyzed the relationship between group delay and the mean phase coherence between 3.5 and 8 Hz for individual participants (Fig. 4B). It was observed that participants showing higher phase coherence tended to have similar group delay: the absolute difference between individual group delay and the mean group delay over participants was negatively correlated with individual phase coherence averaged over 3.5 and 8 Hz (R ¼ À0.467, p ¼ 6 Â 10 À4 , two-tailed Student's t test). This result suggested common group delay for individuals who show reliable phase coherence.

Discussion
The phase-frequency curve is a fundamental character of a system, and here we analyze how the phase-frequency curve of speech envelope-tracking response is modulated by the state of consciousness. The stimulusresponse phase coherence is reduced by the DoC, but it is demonstrated that the linear-phase property can be observed in both healthy individuals and in EMCS/MCS/ UWS patients who exhibit reliable neural synchronization to speech. This result indicates the phase property of envelope-tracking neural activity is not strongly modulated by the state of consciousness, in favor of the evoked response hypothesis (Ding and Simon, 2012b;Power et al., 2012;O'Sullivan et al., 2015;Zou et al., 2021).
What kind of systems can show a linear-phase property? The simplest form of such a system is a delay system, for which the response is simply the stimulus but delayed. Suppose the delay of the system is T. When the stimulus to the system is a sinusoid at f Hz, the response is also an f-Hz sinusoid delayed by T. A delay T corresponds to a 2p Tf phase shift of the f-Hz sinusoid. Therefore, the stimulus-response phase lag is 2p Tf, a linear function of f. The delay T, in this case, is the same as the group delay of the system. More generally, based on the systems theory, if the The phase lag appears to linearly decrease over frequency in a frequency range between 3.5 and 8 Hz. The dotted lines are fitted based on the phase lag between 3.5 and 8 Hz.
stimulus-response phase lag changes linearly across frequency, it indicates that the evoked response has a finite duration and has a symmetric waveform centered at the group delay (Oppenheim et al., 1997).
The current study reveals that between 3.5 and 8 Hz, the envelope-tracking response exhibits the linear-phase property, indicating the EEG response resembles the speech envelope but delayed. More importantly, such linear-phase property and even the group delay is largely unchanged in DoC patients as long as they show reliable envelope-tracking activity. In other words, DoC may result in less precise phase synchronization to speech envelope but does not strongly modulate the phase lag between stimulus and response. The reduced precision in phase synchronization may also be the consequence of the reduction of response amplitude: the envelope-tracking response and spontaneous neural activity are both recorded and the ratio between these two components can contribute to the phase synchronization precision.
These results suggest that cortical areas impaired in DoC patients may disable the envelope-tracking response. Nevertheless, in some patients, the envelope-tracking response is not disabled and the properties of the envelopetracking response are largely maintained. In general, these results are consistent with previous findings that some DoC patients may have preserved bottom-up auditory responses although the response is less reliable than healthy individuals (Fischer et al., 2000;Qin et al., 2008;Gui et al., 2020;Xu et al., 2023).
The frequency range in which the linear phase property is observed, i.e., 3.5-8 Hz, also coincides with the frequency range in which the phase coherence is relatively high. Therefore, it is possible that the phase linearity is lower outside the 3.5-to 8-Hz range since the stimulusresponse phase lag is less reliable outside that frequency range. Previous studies have consistently shown that cortical phase locking to speech significantly decreases above ;8 Hz (e.g., Luo and Poeppel, 2007;Ding and Simon, 2012b), which is potentially attributable to the lack of high-frequency modulations in speech (Ding et al., 2017). Below 8 Hz, the stimulus-response phase coherence is higher than chance until the lowest frequency being analyzed, i.e., 0.5 Hz. In this frequency range, the phase coherence spectrum shows a bimodal pattern, with one peak between 3.5 and 8 Hz and another peak below 1 Hz. In other words, the phase coherence spectrum seems to have Figure 3. Linearity of the phase-frequency curve. A, The second-order derivative of the phase-frequency curve is used to quantify the linearity of the phase-frequency curve. The second-order derivative is 0 if the stimulus-response phase lag changes linearly with frequency. The colored lines on top denote the frequency bins in which the absolute value of the second-order derivative is significantly closer to 0 than chance (p , 0.01, permutation test, FDR corrected). B, The relationship between phase coherence and absolute value of second-order derivative of the phase-frequency curve. The phase coherence and the absolute value of second-order derivative are both averaged between 3.5 and 8 Hz. Participants with higher phase coherence generally show lower absolute value of second order derivatives, i.e., better linearity. Figure 4. Group delay of the speech response. A, Group delay for four populations. Each dot denotes a participant. Between 3.5 and 8 Hz, the group delay is consistent across healthy individuals, but less consistent for the DoC patients. B, The relationship between group delay and phase coherence for individuals. The x-axis is the phase coherence averaged between 3.5 and 8 Hz. The y-axis on the left is the mean phase difference between neighboring frequency bins, and the y-axis on the right shows the group delay. Participants with higher phase coherence generally show consistent group delay. a dip around 2 Hz and a similar trend has been observed in previous studies (Koskinen and Seppä, 2014;Bourguignon et al., 2020). Although the mechanism underlying the 2-Hz dip remain unclear, it is possible that it marks a transition in the neural encoding scheme.
Together with a number of previous studies (Lalor et al., 2009;Ding and Simon, 2012a;Zou et al., 2021), the current study suggests that the neural mechanisms generating envelope-tracking neural activity can be well approximated as a linear system. This linear-system view, however, does not suggest that top-down factors, such as attention, cannot modulate envelope-tracking activity. Instead, many studies that analyze attention modulation of envelopetracking activity model the envelope-tracking response using a linear system, e.g., using the temporal response function (TRF) approach (Lalor et al., 2009;Ding and Simon, 2012a;Brodbeck et al., 2018), and these studies show that the response gain can be enhanced by selective attention (Ding and Simon, 2012b;Mesgarani and Chang, 2012;E.M. Zion Golumbic et al., 2013b). On top of the response gain change, it is also possible that more active speech processing can engage more sophisticated mechanisms in line with the oscillation phase-resetting hypothesis. This possibility, however, has to be addressed by future studies. In the current study, speech is presented in a quiet environment and previous studies have shown attention only minimally modulate the envelope-tracking response (Kong et al., 2014;Ding et al., 2018;Lu et al., 2023).
In summary, the current results suggest that the neural generator for envelope-tracking activity is more strongly shaped by bottom-up auditory processing than top-down feedback from consciousness-related cortical areas that are impaired by DoC.